A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 8 , 2 )
( 7 , 4 )
( 1 , 3 )
( 5 , 6 )
( 2 , 5 )
( 6 , 2 )
( 6 , 7 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
An \(x\) value repeats with different \(y\) values, so \(y\) is not a function of \(x\). For example: (6, 2) and (6, 7)
Also, a \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). For example: (8, 2) and (6, 2)
We would need both to be function of the other to have a one-to-one function. Neither is, so we don’t even have a function in either direction.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 1 , 3 )
( 4 , 1 )
( 2 , 9 )
( 5 , 4 )
( 6 , 5 )
( 6 , 5 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
Every repeated \(x\) value is matched with a consistent (also repeating) \(y\), and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the list is consistent with a one-to-one function.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 8 , 7 )
( 4 , 5 )
( 3 , 3 )
( 4 , 5 )
( 1 , 5 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
Every repeated \(x\) value is matched with a consistent (also repeating) \(y\), so \(y\) is a function of \(x\).
A \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). For example: (4, 5) and (1, 5)
Because \(x\) is not a function of \(y\), this list is inconsistent with a one-to-one function.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 5 , 1 )
( 6 , 8 )
( 3 , 4 )
( 1 , 4 )
( 1 , 4 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
Every repeated \(x\) value is matched with a consistent (also repeating) \(y\), so \(y\) is a function of \(x\).
A \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). For example: (3, 4) and (1, 4)
Because \(x\) is not a function of \(y\), this list is inconsistent with a one-to-one function.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 9 , 4 )
( 6 , 5 )
( 6 , 5 )
( 9 , 4 )
( 4 , 2 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
Every repeated \(x\) value is matched with a consistent (also repeating) \(y\), and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the list is consistent with a one-to-one function.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 4 , 7 )
( 9 , 9 )
( 5 , 8 )
( 7 , 3 )
( 8 , 5 )
( 2 , 1 )
( 5 , 8 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
Every repeated \(x\) value is matched with a consistent (also repeating) \(y\), and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the list is consistent with a one-to-one function.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 3 , 2 )
( 5 , 6 )
( 2 , 4 )
( 4 , 9 )
( 8 , 3 )
( 8 , 3 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
Every repeated \(x\) value is matched with a consistent (also repeating) \(y\), and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the list is consistent with a one-to-one function.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 5 , 4 )
( 2 , 1 )
( 6 , 6 )
( 6 , 4 )
( 8 , 8 )
( 8 , 7 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
An \(x\) value repeats with different \(y\) values, so \(y\) is not a function of \(x\). For example: (8, 8) and (8, 7)
Also, a \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). For example: (5, 4) and (6, 4)
We would need both to be function of the other to have a one-to-one function. Neither is, so we don’t even have a function in either direction.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 7 , 3 )
( 3 , 8 )
( 5 , 6 )
( 1 , 6 )
( 1 , 9 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
An \(x\) value repeats with different \(y\) values, so \(y\) is not a function of \(x\). For example: (1, 6) and (1, 9)
Also, a \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). For example: (5, 6) and (1, 6)
We would need both to be function of the other to have a one-to-one function. Neither is, so we don’t even have a function in either direction.
Question
A list of inputs and outputs is expressed as \((x,y)\) pairs.
( 3 , 3 )
( 8 , 7 )
( 1 , 9 )
( 4 , 5 )
( 1 , 9 )
( 7 , 6 )
( 1 , 9 )
Is this list consistent with \(y\) being a function of \(x\)?
Is this list consistent with \(x\) being a function of \(y\)?
Is this list consistent with a one-to-one function?
Solution
Every repeated \(x\) value is matched with a consistent (also repeating) \(y\), and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the list is consistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, so \(y\) is a function of \(x\). The graph passes the vertical line test.
A \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). The graph fails the horizontal line test. For example: (8, 3) and (6, 3)
Because \(x\) is not a function of \(y\), these points are inconsistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
An \(x\) value repeats with different \(y\) values, so \(y\) is not a function of \(x\). The graph fails the vertical-line test. For example: (10, 1) and (10, 8)
Every \(y\) value has only one \(x\) value, so \(x\) is a function of \(y\). The graph passes the horizontal line test.
Because \(y\) is not a function of \(x\), these points are inconsistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, so \(y\) is a function of \(x\). The graph passes the vertical line test.
A \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). The graph fails the horizontal line test. For example: (10, 1) and (9, 1)
Because \(x\) is not a function of \(y\), these points are inconsistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, and vice versa. The graph passes both the vertical-line and horizontal-line tests. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the points are consistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
An \(x\) value repeats with different \(y\) values, so \(y\) is not a function of \(x\). The graph fails the vertical line test. For example: (4, 9) and (4, 3)
Also, a \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). The graph fails the horizontal line test. For example: (3, 9) and (4, 9)
We would need both to be function of the other to have a one-to-one function. Neither is, so we don’t even have a function in either direction.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, and vice versa. The graph passes both the vertical-line and horizontal-line tests. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the points are consistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, and vice versa. The graph passes both the vertical-line and horizontal-line tests. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the points are consistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, so \(y\) is a function of \(x\). The graph passes the vertical line test.
A \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). The graph fails the horizontal line test. For example: (5, 6) and (6, 6)
Because \(x\) is not a function of \(y\), these points are inconsistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, so \(y\) is a function of \(x\). The graph passes the vertical line test.
A \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). The graph fails the horizontal line test. For example: (1, 5) and (7, 5)
Because \(x\) is not a function of \(y\), these points are inconsistent with a one-to-one function.
Question
Are these points consistent with \(y\) being a function of \(x\)?
Are these points consistent with \(x\) being a function of \(y\)?
Are these points consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
Every \(x\) value has only one \(y\) value, so \(y\) is a function of \(x\). The graph passes the vertical line test.
A \(y\) value repeates with different \(x\) values, so \(x\) is not a function of \(y\). The graph fails the horizontal line test. For example: (3, 4) and (10, 4)
Because \(x\) is not a function of \(y\), these points are inconsistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
Every \(x\) value has only one connection, and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the connections are consistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
An \(x\) value has two connections, so \(y\) is not a function of \(x\). For example: (2, 6) and (2, 1)
Every \(y\) value has only one connection, so \(x\) is a function of \(y\).
Because \(y\) is not a function of \(x\), these connections are inconsistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
Every \(x\) value has only one connection, and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the connections are consistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
Every \(x\) value has only one connection, and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the connections are consistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
Every \(x\) value has only one connection, so \(y\) is a function of \(x\).
A \(y\) value has two connections, so \(x\) is not a function of \(y\). For example: (0, 2) and (1, 2)
Because \(x\) is not a function of \(y\), these connections are inconsistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
An \(x\) value has two different connections, so \(y\) is not a function of \(x\). For example: (4, 5) and (4, 0)
Also, a \(y\) value has two different connections, so \(x\) is not a function of \(y\). For example: (5, 4) and (7, 4)
We would need both to be function of the other to have a one-to-one function. Neither is, so we don’t even have a function in either direction.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
An \(x\) value has two connections, so \(y\) is not a function of \(x\). For example: (4, 2) and (4, 8)
Every \(y\) value has only one connection, so \(x\) is a function of \(y\).
Because \(y\) is not a function of \(x\), these connections are inconsistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
Every \(x\) value has only one connection, and vice versa. This means \(y\) is a function of \(x\) and \(x\) is a function of \(y\), and the connections are consistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
An \(x\) value has two connections, so \(y\) is not a function of \(x\). For example: (2, 2) and (2, 3)
Every \(y\) value has only one connection, so \(x\) is a function of \(y\).
Because \(y\) is not a function of \(x\), these connections are inconsistent with a one-to-one function.
Question
Are these connections consistent with \(y\) being a function of \(x\)?
Are these connections consistent with \(x\) being a function of \(y\)?
Are these connections consistent with a one-to-one function?
Solution
If any value of \(x\) has two different connections, then \(y\) is not a function of \(x\). If any value of \(y\) has two different connections, then \(x\) is not a function of \(y\).
An \(x\) value has two connections, so \(y\) is not a function of \(x\). For example: (2, 9) and (2, 6)
Every \(y\) value has only one connection, so \(x\) is a function of \(y\).
Because \(y\) is not a function of \(x\), these connections are inconsistent with a one-to-one function.
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Is this curve consistent with \(y\) being a function of \(x\)?
Is this curve consistent with \(x\) being a function of \(y\)?
Is this curve consistent with a one-to-one function?
Solution
It is best to visualize the vertical line test and the horizontal line test. If you can draw a vertical line through 2 (or more) points, then \(y\) is not a function of \(x\). If you can draw a horizontal line through 2 (or more) points, then \(x\) is not a function of \(y\).
The function is one-to-one if and only if \(y\) is a function of \(x\) and \(x\) is a function of \(y\).
Below, if the function is not one-to-one, some failed line tests are shown:
Question
Let function \(f\) be defined as follows:
\[f(x) = 2 x^{2} + 5 x + 4\]Evaluate\(f(6.11)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(6.11\) in the definition of \(f\).
\[2 (6.11)^{2} + 5 (6.11) + 4\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = - 4 x^{2} + 4 x + 3\]Evaluate\(f(-3.29)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(-3.29\) in the definition of \(f\).
\[- 4 (-3.29)^{2} + 4 (-3.29) + 3\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = - 2 x^{2} - 5 x - 3\]Evaluate\(f(-6.6)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(-6.6\) in the definition of \(f\).
\[- 2 (-6.6)^{2} - 5 (-6.6) - 3\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = - 2 x^{2} + 3 x + 5\]Evaluate\(f(0.24)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(0.24\) in the definition of \(f\).
\[- 2 (0.24)^{2} + 3 (0.24) + 5\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = 3 x^{2} + 4 x - 5\]Evaluate\(f(-7.27)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(-7.27\) in the definition of \(f\).
\[3 (-7.27)^{2} + 4 (-7.27) - 5\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = - 5 x^{2} - 2 x - 3\]Evaluate\(f(-0.56)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(-0.56\) in the definition of \(f\).
\[- 5 (-0.56)^{2} - 2 (-0.56) - 3\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = - 2 x^{2} + 2 x + 4\]Evaluate\(f(9.08)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(9.08\) in the definition of \(f\).
\[- 2 (9.08)^{2} + 2 (9.08) + 4\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = - 3 x^{2} - 5 x + 5\]Evaluate\(f(2.29)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(2.29\) in the definition of \(f\).
\[- 3 (2.29)^{2} - 5 (2.29) + 5\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = - 3 x^{2} - 2 x + 4\]Evaluate\(f(-1.82)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(-1.82\) in the definition of \(f\).
\[- 3 (-1.82)^{2} - 2 (-1.82) + 4\]
You’ll want to use a calculator.
Question
Let function \(f\) be defined as follows:
\[f(x) = 5 x^{2} + 4 x - 3\]Evaluate\(f(4.18)\).
You can round (or truncate) at the tenths place.
Solution
Replace all \(x\) variables with \(4.18\) in the definition of \(f\).
\[5 (4.18)^{2} + 4 (4.18) - 3\]
You’ll want to use a calculator.
Question
A function \(f\) is graphed below.
Evaluate \(f(7)\).
Solution
Find the correct point on the graph where \(x=7\).
\[f(7)=1\]
Question
A function \(f\) is graphed below.
Evaluate \(f(7)\).
Solution
Find the correct point on the graph where \(x=7\).
\[f(7)=6\]
Question
A function \(f\) is graphed below.
Evaluate \(f(3)\).
Solution
Find the correct point on the graph where \(x=3\).
\[f(3)=7\]
Question
A function \(f\) is graphed below.
Evaluate \(f(5)\).
Solution
Find the correct point on the graph where \(x=5\).
\[f(5)=9\]
Question
A function \(f\) is graphed below.
Evaluate \(f(8)\).
Solution
Find the correct point on the graph where \(x=8\).
\[f(8)=3\]
Question
A function \(f\) is graphed below.
Evaluate \(f(9)\).
Solution
Find the correct point on the graph where \(x=9\).
\[f(9)=5\]
Question
A function \(f\) is graphed below.
Evaluate \(f(8)\).
Solution
Find the correct point on the graph where \(x=8\).
\[f(8)=2\]
Question
A function \(f\) is graphed below.
Evaluate \(f(7)\).
Solution
Find the correct point on the graph where \(x=7\).
\[f(7)=9\]
Question
A function \(f\) is graphed below.
Evaluate \(f(8)\).
Solution
Find the correct point on the graph where \(x=8\).
\[f(8)=1\]
Question
A function \(f\) is graphed below.
Evaluate \(f(5)\).
Solution
Find the correct point on the graph where \(x=5\).
\[f(5)=8\]
Question
A function \(f\) is graphed below.
If \(f(x)=8\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=8\).
\[f(6)=8\]
Question
A function \(f\) is graphed below.
If \(f(x)=7\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=7\).
\[f(8)=7\]
Question
A function \(f\) is graphed below.
If \(f(x)=8\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=8\).
\[f(1)=8\]
Question
A function \(f\) is graphed below.
If \(f(x)=4\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=4\).
\[f(5)=4\]
Question
A function \(f\) is graphed below.
If \(f(x)=4\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=4\).
\[f(9)=4\]
Question
A function \(f\) is graphed below.
If \(f(x)=7\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=7\).
\[f(9)=7\]
Question
A function \(f\) is graphed below.
If \(f(x)=3\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=3\).
\[f(2)=3\]
Question
A function \(f\) is graphed below.
If \(f(x)=4\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=4\).
\[f(8)=4\]
Question
A function \(f\) is graphed below.
If \(f(x)=7\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=7\).
\[f(5)=7\]
Question
A function \(f\) is graphed below.
If \(f(x)=4\), then find \(x\).
Solution
Find the correct point on the graph where \(f(x)=4\).
\[f(9)=4\]
Question
Let function \(f\) be defined as follows:
\[f(x) ~=~ - 5 x^{3} + 5 x^{2} - 2 x + 4\]
Which of the following expressions is equivalent to \(f(-a)\)?
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has rotational symmetry around the origin.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has neither reflective nor rotational symmetry.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has reflective symmetry over the \(y\) axis.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has reflective symmetry over the \(y\) axis.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has reflective symmetry over the \(y\) axis.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has neither reflective nor rotational symmetry.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has neither reflective nor rotational symmetry.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has rotational symmetry around the origin.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has neither reflective nor rotational symmetry.
A function \(f\) is even if and only if \(f(-x)=f(x)\) for all \(x\). In an even function, opposite inputs give equal outputs. An even function has reflective symmetry over the vertical axis.
A function \(f\) is odd if and only if \(f(-x)=-f(x)\) for all \(x\). In an odd function, opposite inputs give opposite outputs. An odd function has rotational symmetry around the origin.
A function can also be neither even nor odd.
A function \(f\) is graphed below.
Is the function’s graph consistent with the function being even, odd, or neither?
Even
Odd
Neither
Solution
The graph has rotational symmetry around the origin.
The function is odd.
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([4,\,8]\), and the range is from the minimum \(y\) to the maximum \(y\): \([1,\,6]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([1,\,8]\), and the range is from the minimum \(y\) to the maximum \(y\): \([4,\,9]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([3,\,8]\), and the range is from the minimum \(y\) to the maximum \(y\): \([1,\,9]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([3,\,9]\), and the range is from the minimum \(y\) to the maximum \(y\): \([1,\,7]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([3,\,9]\), and the range is from the minimum \(y\) to the maximum \(y\): \([1,\,7]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([2,\,6]\), and the range is from the minimum \(y\) to the maximum \(y\): \([1,\,9]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([1,\,8]\), and the range is from the minimum \(y\) to the maximum \(y\): \([3,\,9]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([2,\,9]\), and the range is from the minimum \(y\) to the maximum \(y\): \([1,\,8]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([1,\,8]\), and the range is from the minimum \(y\) to the maximum \(y\): \([2,\,9]\).
Question
A function \(f\) is graphed below.
Determine the domain and range. Note: wikipedia suggests using “image” instead of “range”.
Because the curve is continuous, the domain is from the minimum \(x\) value to the maximum \(x\) value: \([3,\,8]\), and the range is from the minimum \(y\) to the maximum \(y\): \([1,\,9]\).
Question
Let function \(f\) be defined as follows:
\[f(x) ~=~ 5 x^{2} - 2 x + 2\]
Which of the following expressions is equivalent to \(f(a+h)\)?
\[f(a+h) ~=~ - 2 a^{2} - 4 a h - 9 a - 2 h^{2} - 9 h + 2\]
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=0\) and \(x=10\).
Notice the orange segment has length of 4 and the violet segment has length of 10. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=5\) and \(x=9\).
Notice the orange segment has length of 2 and the violet segment has length of 4. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=4\) and \(x=9\).
Notice the orange segment has length of 2 and the violet segment has length of 5. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=9\) and \(x=10\).
Notice the orange segment has length of 5 and the violet segment has length of 1. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=2\) and \(x=4\).
Notice the orange segment has length of 8 and the violet segment has length of 2. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=6\) and \(x=10\).
Notice the orange segment has length of 4 and the violet segment has length of 4. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=2\) and \(x=3\).
Notice the orange segment has length of 5 and the violet segment has length of 1. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=5\) and \(x=10\).
Notice the orange segment has length of 4 and the violet segment has length of 5. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=5\) and \(x=7\).
Notice the orange segment has length of 7 and the violet segment has length of 2. The formula for average rate of change is “rise over run”.
Question
This question is about average rate of change. For function \(f(x)\), its average rate of change between \(x=a\) and \(x=b\) equals a quotient of differences:
\[\text{ave rate of change} = \frac{f(b)-f(a)}{b-a} \]
A function \(f\) is graphed below.
Find the average rate of change between \(x=7\) and \(x=10\).
Notice the orange segment has length of 7 and the violet segment has length of 3. The formula for average rate of change is “rise over run”.
Question
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 2 x^{2} - 3 x + 4\]Evaluate the average rate of change of \(f(x)\) at \(a=3\) with a step size \(h=0.01\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 4 x^{2} + 2 x - 2\]Evaluate the average rate of change of \(f(x)\) at \(a=6\) with a step size \(h=0.01\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = 3 x^{2} - 5 x - 2\]Evaluate the average rate of change of \(f(x)\) at \(a=-2\) with a step size \(h=0.1\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 2 x^{2} - 4 x + 4\]Evaluate the average rate of change of \(f(x)\) at \(a=-2\) with a step size \(h=0.001\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 5 x^{2} - 2 x + 4\]Evaluate the average rate of change of \(f(x)\) at \(a=9\) with a step size \(h=0.1\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 2 x^{2} + 5 x - 4\]Evaluate the average rate of change of \(f(x)\) at \(a=-10\) with a step size \(h=0.001\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = 2 x^{2} + 5 x - 3\]Evaluate the average rate of change of \(f(x)\) at \(a=9\) with a step size \(h=0.01\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 5 x^{2} - 4 x - 3\]Evaluate the average rate of change of \(f(x)\) at \(a=-2\) with a step size \(h=0.001\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 5 x^{2} + 4 x - 3\]Evaluate the average rate of change of \(f(x)\) at \(a=5\) with a step size \(h=0.01\).
You can round (or truncate) at the hundredths place.
We often find the average rate of change over a small interval, to approximate the instantaneous rate of change (think of a speedometer). The step size, \(h\), is the width of the interval, so we find the average rate of change of \(f(x)\) between \(a\) and \(a+h\):
\[\text{AROC} = \frac{f(a+h)-f(a)}{h}\]
Let function \(f\) be defined as follows:
\[f(x) = - 3 x^{2} - 5 x - 2\]Evaluate the average rate of change of \(f(x)\) at \(a=0\) with a step size \(h=0.001\).
You can round (or truncate) at the hundredths place.